705 research outputs found
Homotopical stable ranks for Banach algebras
The connected stable rank and the general stable rank are homotopy invariants
for Banach algebras, whereas the Bass stable rank and the topological stable
rank should be thought of as dimensional invariants. This paper studies the two
homotopical stable ranks, viz. their general properties as well as specific
examples and computations. The picture that emerges is that of a strong
affinity between the homotopical stable ranks, and a marked contrast with the
dimensional ones.Comment: 23 pages, final versio
Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities
We prove a family of uncertainty inequalities on fairly general groups
and homogeneous spaces, both in the smooth and in the discrete setting. The
crucial point is the proof of the endpoint, which is derived from a
general weak isoperimetric inequality.Comment: 17 page
Spectral morphisms, K-theory, and stable ranks
We give a brief account of the interplay between spectral morphisms,
K-theory, and stable ranks in the context of Banach algebras.Comment: 12 pages; to appear in the Proceedings of the Workshop on
Noncommutative Geometry (Fields Institute, Toronto 2008
Hypertoric category O
We study the representation theory of the invariant subalgebra of the Weyl
algebra under a torus action, which we call a "hypertoric enveloping algebra."
We define an analogue of BGG category O for this algebra, and identify it with
a certain category of sheaves on a hypertoric variety. We prove that a regular
block of this category is highest weight and Koszul, identify its Koszul dual,
compute its center, and study its cell structure. We also consider a collection
of derived auto-equivalences analogous to the shuffling and twisting functors
for BGG category O.Comment: 65 pages, TikZ figures (PDF is recommended; DVI will not display
correctly on all computers); v3: switched terminology for twisting and
shuffling; final version; v4: small correction in definition of standard
module
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